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Shape Optimization for Stokes Flows using Conformal Metrics
Author(s) -
Leithäuser Christian,
Feßler Robert,
Pinnau René
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010283
Subject(s) - conformal map , metric (unit) , computation , shape optimization , domain (mathematical analysis) , shear stress , flow (mathematics) , stokes flow , mathematics , geometry , conformal geometry , differential (mechanical device) , differential geometry , mathematical analysis , mathematical optimization , physics , algorithm , mechanics , conformal symmetry , engineering , finite element method , operations management , thermodynamics
We derive a shape optimization approach for a two‐dimensional Stokes flow problem. Our goal is to compute a geometry whose wall shear stress is L 2 ‐close to a desired target stress. Computations are carried out on a fixed domain, while shape variations are described through conformal metric changes. Tools from differential geometry are used to handle metric dependent operators. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)